De Novo Designed Non-Local Beta Sheet Proteins

ABSTRACT

Beta-sheet forming polypeptides at least 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% identical to the amino acid sequence selected from the group consisting of SEQ ID NOS:1-24 are disclosed, together with their use and methods for designing beta-sheet forming polypeptides.

CROSS REFERENCE

This application claims priority to U.S. Provisional Patent Application Ser. No. 62/926,203 filed Oct. 25, 2019, incorporated by reference herein in its entirety.

SEQUENCE LISTING STATEMENT

A computer readable form of the Sequence Listing is filed with this application by electronic submission and is incorporated into this application by reference in its entirety. The Sequence Listing is contained in the file created on Oct. 8, 2020, having the file name “19-1613-US_Sequence-Listing_SEQ.txt” and is 18.3 kb in size.

BACKGROUND

β-sheet proteins carry out critical functions in biology, and hence are attractive scaffolds for computational protein design. Despite this potential, de novo design of all β-sheet proteins from first principles lags far behind the design of all-α or mixed αβ domains due to their non-local nature and tendency of exposed β-strand edges to aggregate.

SUMMARY

In one aspect, the disclosure provides polypeptides. comprising an amino acid sequence at least 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% identical to the amino acid sequence selected from the group consisting of SEQ ID NOS:1-24, wherein the polypeptide forms a beta-sheet. In one embodiment, the polypeptide may comprise two beta-sheets packing against each other forming a double-stranded beta-helix formed by 8 antiparallel beta-strands. In another embodiment, the polypeptide may comprise an amino acid sequence at least 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% identical to the amino acid sequence selected from the group consisting of SEQ ID NOS:10, 11, and 20-24. In one embodiment, amino acid changes from the reference polypeptide do not include changes in proline residues present in loop connections between beta strands. In another embodiment, amino acid changes from the reference polypeptide do not include changes in polar amino acid residues present in loop connections between beta strands capable of forming hydrogen bonds to the loop backbone. In a further embodiment, amino acid changes from the reference polypeptide do not include changes in hydrophobic amino acid residues present in the loop connections and adjacent to the polar amino acid residues between beta strands capable of forming hydrogen bonds to the loop backbone.

In one embodiment, amino acid changes from the reference polypeptide do not include changes in hydrophobic amino acid residues stabilizing the polypeptide core. In another embodiment, amino acid changes from the reference polypeptide are conservative amino acid substitutions.

In other aspects, the disclosure provides nucleic acids encoding the polypeptide of any embodiment or combination of embodiments of the disclosure; expression vectors comprising the nucleic acids of the disclosure linked to a control sequence; host cells comprising the nucleic acid and/or expression vector of the disclosure; cells expressing the polypeptide of any embodiment or combination of embodiments of the disclosure; and pharmaceutical composition comprising the polypeptide of any embodiment or combination of embodiments of the disclosure and a pharmaceutically acceptable carrier.

In another aspect, the disclosure provides methods for use of the polypeptide of any embodiment or combination of embodiments of the disclosure for any suitable purpose, including but not limited to as scaffolds for virus capsids and antibodies and to transport hydrophobic molecules, for use in recognition and enzymatic processing of carbohydrates; incorporating metal, ligand-binding and active sites.

In another aspect, the disclosure provides methods for designing polypeptides that form a double-stranded β-helix formed by 8 antiparallel β-strands, comprising the steps of any embodiment or combinations of embodiments disclosed herein.

DESCRIPTION OF THE FIGURES

FIG. 1A-1H. Constraints on β-arch geometry. (A) Sidechain directionality in the β-arch. (B) comparison between β-hairpin and β-arch; the CαCβ and d vectors used to define the orientation of the two adjacent sidechains are indicated. The four possible sidechain directionality patterns are on the right. (C) Turn type dependence of β-arch sidechain patterns. Loops on the y-axis are described by their ABEGO torsion bins (FIG. 4). Most of the loops adopt only one of the four possible sidechain patterns. (D) Frequency of the most common loops for each of the four β-arch sidechain patterns. There are strong preferences, for example BBGB is strongly associated with the “↓↑” pattern, whereas ABB is strongly associated with the “↓↓” pattern (E). Only loops with bending <120 degrees (Methods) and containing between 1 and 5 amino acids were considered in this analysis. (F) Two stacked β-arches having in-register strand pairing form β-arcades. (G) Since strand pairs of the β-arcade are in-register, the sidechains adjacent to one β-arch loop must have the same orientation as the paired sidechains that are adjacent to the second β-arch loop, and therefore not all loop pairs are allowed. (H) Example of a β-arcade formed by two common β-arches with compatible sidechain patterns.

FIG. 2A-2E. Double-stranded β-helix topology specification. (A) The double-stranded β-helix fold consists of two 4-stranded antiparallel β-sheets with 6 β-arch and 1β-hairpin connections. Pairs of β-arches forming the three β-arcades are highlighted on the right. (B) Topology diagram of a designed double-stranded 3-helix with all β-strand pairs in register. Sidechain Cβ positions oriented toward the inner and outer faces of the β-helix are represented with up and down black arrows with rounded tips, respectively. (C) Definition of β-arcade register shift varied during conformational sampling. The β-arcade register shift (between β-arcades 1 and 3) is determined by the register of β-strand pairs S₃/S₈ and S₄/S₇, and the lengths of β-strands S₃, S₄, S₈ and S₇ (Methods). In this example β-strand pairs S₃/S₈ and S₄/S₇ each have a two residue register shift, resulting in an overall β-arcade register shift of 4 residues. Loops are omitted to facilitate visualization. (D) Example of a design model with all β-strand pairs in register forming a sandwich-like structure. (E) Example of a design model with register shifts between β-arcades 1 and 3 forming a barrel-like structure.

FIG. 3A-3G. Computational design and characterization of BH_10. (A) Calculated BH_10 folding energy landscape. Each dot represents the lowest energy structure obtained from ab initio folding trajectories starting from an extended chain, biased forward folding trajectories or local relaxation of the designed structure; x-axis is the Cα-root mean squared deviation (RMSD) from the designed model; the y-axis, the Rosetta™ all-atom energy. (B) Far-ultraviolet circular dichroism spectra. (C) Design model. The topology scheme of the design model is shown on the left, describing ABEGO torsion bins of all loop connections. (D) Backbone hydrogen bonding of β-arcade 1. (E) Sidechain interactions of N65 with backbone and sidechains form a hydrogen-bonded network in β-arcade 3. (F) Contact order of de novo protein domains computationally designed to date confirmed by high resolution structure determination; all-α, αβ and all-β. BH_10 stands out with a contact order of 35.8 for a chain length of 78 residues. (G) Contact map illustrating the large sequence separation of the contacts present in the BH_10 topology.

FIG. 4. Coarse-grained representation of the Ramachandran plot based on ABEGO torsion bins. ABEGO torsion bins provide a convenient way to classify the backbone geometry of protein residues based on the Ramachandran plot region of their ϕ/ψ dihedrals. “A” corresponds to the right-handed α-helix, “B” to the extended region typical of β-strands, “E” to the extended region with a positive ϕ dihedral, “G” to a left-handed α-helix (mostly accessible by L-glycine). The “O” bin is assigned for the cis peptide conformation (torsion around the peptide bond with the preceding residue, Cα(i)-N(i)-C(i−1)-Cα(i−1), below 90 degrees). Plotted data was collected from the residue torsional values of all β-arch loops from a non-redundant set of naturally occurring protein structures. Analysis of these loops revealed the sidechain pattern preferences of different loop ABEGO types, a critical feature for design.

FIG. 5A-5B. SEC-MALS analysis of (A) BH_10 and (B) BH_11 designs. Both proteins are monodisperse and have estimated molecular weights in good agreement with the theoretical value of the monomers.

FIG. 6A-6C. Experimental characterization of the designed protein BH_11. (A) Cartoon representation of the design model. (B) Calculated folding energy landscape. Each dot represents the lowest energy structure obtained from ab initio folding trajectories starting from an extended chain, biased forward folding trajectories or local relaxation of the designed structure; x-axis shows the Cα-root mean squared deviation (RMSD) from the designed model; the y-axis shows the Rosetta™ all-atom energy. (C) Far-ultraviolet circular dichroism spectra.

FIG. 7. Surface salt bridges of design BH_10. Salt bridges of the computational model. Most of these salt bridges correspond to residues involved in the pairing between β-arcades 1 and 3 (E33:R64, E35:R62 and E78:R23).

FIG. 8A-8B. Loop sequences and patterns of design BH_10. (A) designed protein sequence (SEQ ID NO:10) and ABEGO strings of loops (β-strands, β-arches and the β-hairpin). Critical residues determining the sidechain patterns of β-arches are highlighted. (B) All-atom stereo representation of the design with backbone hydrogen bonding and salt bridge interactions highlighted. Critical loop positions, such as prolines in β-arches or the central β-hairpin residues, are also indicated.

FIG. 9A-9B. Naturally occurring proteins with most similar structures or sequences to design BH_10. (A) Three closest structural analogs identified with DALI (Holm, L. & Laakso, L. M. Nucleic Acids Res. 44, W351-5, 2016) are homodimers. The sequence identity over structurally aligned regions ranged from 7 to 19%. (B) Three protein domains most similar in sequence and with structure available, as identified with HHpred (Zimmermann, L. et al. J. Mol. Biol. 430, 2237-2243, 2018), are also homodimers or part of a larger structure. For these three proteins the sequence identity with BH_10 was 21% and E-values ranged between 0.14 and 0.39. The natural proteins identified all exhibit more irregular secondary structures, longer loops and extra elements building protein interfaces.

FIG. 10A-10I. Sequence determinants of β-arch formation. For the energy landscapes of different types of mutations we calculated the frequency of formation of β-hairpins between every two consecutive β-strands. Increases of β-hairpin formation were correlated with a decrease of near native sampling. (A, D, G, I) Calculated energy landscapes for mutants assessing different types of interactions are compared with the landscape of BH_10. (B, E, H) Effect of mutations on β-strand pairing. Mutated loop connections are labeled with the corresponding amino acid substitution. Most of the mutations increase sampling of more local β-hairpin connections. Connection S4-S5 corresponds to the central β-hairpin of the β-helix. (C) Sidechain packing interactions stabilizing β-arch loop connections that when mutated to alanine decrease β-arch stability and favor β-hairpin sampling. Mutant V18A favors hairpin sampling in the neighboring β-arch of the same β-arcade. (F) Sidechain-backbone hydrogen-bonding interactions stabilizing β-arch loop geometry; upon removal by alanine substitutions β-hairpin sampling increases. (E) Mutations in the S6-S7 and S7-S8 connections favors sampling of β-hairpins between S6 and S8.

DETAILED DESCRIPTION

As used herein, the amino acid residues are abbreviated as follows: alanine (Ala; A), asparagine (Asn; N), aspartic acid (Asp; D), arginine (Arg; R), cysteine (Cys; C), glutamic acid (Glu; E), glutamine (Gln; Q), glycine (Gly; G), histidine (His; H), isoleucine (Ile; I), leucine (Leu; L), lysine (Lys; K), methionine (Met; M), phenylalanine (Phe; F), proline (Pro; P), serine (Ser; S), threonine (Thr; T), tryptophan (Trp; W), tyrosine (Tyr; Y), and valine (Val; V).

All references cited are herein incorporated by reference in their entirety. Within this application, unless otherwise stated, the techniques utilized may be found in any of several well-known references such as: Molecular Cloning: A Laboratory Manual (Sambrook, et al., 1989, Cold Spring Harbor Laboratory Press), Gene Expression Technology (Methods in Enzymology, Vol. 185, edited by D. Goeddel, 1991. Academic Press, San Diego, Calif.), “Guide to Protein Purification” in Methods in Enzymology (M. P. Deutshcer, ed., (1990) Academic Press, Inc.); PCR Protocols: A Guide to Methods and Applications (Innis, et al. 1990. Academic Press, San Diego, Calif.), Culture of Animal Cells: A Manual of Basic Technique, 2^(nd) Ed. (R. I. Freshney. 1987. Liss, Inc. New York, N.Y.), Gene Transfer and Expression Protocols, pp. 109-128, ed. E. J. Murray, The Humana Press Inc., Clifton, N.J.), and the Ambion 1998 Catalog (Ambion, Austin, Tex.).

As used herein, the singular forms “a”, “an” and “the” include plural referents unless the context clearly dictates otherwise.

All embodiments of any aspect of the disclosure can be used in combination, unless the context clearly dictates otherwise.

Unless the context clearly requires otherwise, throughout the description and the claims, the words ‘comprise’, ‘comprising’, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”. Words using the singular or plural number also include the plural and singular number, respectively. Additionally, the words “herein,” “above,” and “below” and words of similar import, when used in this application, shall refer to this application as a whole and not to any particular portions of the application.

In one aspect, the disclosure provides polypeptide comprising an amino acid sequence at least 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% identical to the amino acid sequence selected from the group consisting of SEQ ID NOS:1-24, wherein the polypeptide forms a beta-sheet. As disclosed in the attached appendices, the inventors have provided the first accurate de novo design of beta-sheet polypeptides with the jelly roll fold. Beta-strand positions are shown in Table 1 in bold and underlined font, with non-highlighted residue between the beta strands are loop connections between the beta strands.

Such beta-sheet polypeptides can be used, for example, as protein scaffolds for metal, ligand-binding or enzyme active sites. The ability to design these “de novo” allows tailoring their structure for target recognition sites with both high structural accuracy and thermostability.

TABLE 1 Design name Amino acid sequence BH_1 P ETKTYRF TPG EEREYE ENT DVEVEV NHD MEITV NG QTQRY TPG TSV SEQ ID NO: 1 RV PPG SRVRIRV NDD VKVNWHE R BH_2 Q HTRTYRL TPG EEQEFKY NTP MTMHVEV NTD VEIEY NG KEQRY PPG T SEQ ID NO: 2 EVEIEVR PGT KVRIKV NTD VRVEIRE N BH_3 P ETRTYRF TPG EEREFEF DTN VEFRF DSD VEVTV NG QTTRV PPG SSV SEQ ID NO: 3 EV PPG SRIRIRV NTD LQVEVRR R BH_4 P ETKTYRF TPG EEREFEH DTN VKWKF NTD VEIER NG ERTRF TPG EEV SEQ ID NO: 4 EV PPG TRVRIRV NTD VQFTLER N BH_5 P ERREIRL SPG ERYTFTV DTD VQFRV EKP VRVRH DG TETEY KPG THL SEQ ID NO: 5 RL PPG TSVTFEV DTD VRFEIQR N BH_6 P ERREIRL SPG ERYTFTV DTP VQFRV EKP VRVRY DG TETEL KPGSHL SEQ ID NO: 6 RL PPG TSITFEV DTP VR FEIQR N BH_7 S RYEITG NPG TRVELRE NPG SRVKS NAPG RSER NG EHRTW NPG ESRT SEQ ID NO: 7 S NRP STMEVES DGP ISIEIR E BH_8 E SKKITV NAGER MTLHL NAG TEVRS EGP GREHS NG QTQQW PPG STIR SEQ ID NO: 8 S DQP TTTTF ESDRP LTLEVR Q BH_9 K TKTYTV NPGE KVTITM NPG DEMTA EGP VTSRA RG QEQTV NPG ETVR SEQ ID NO: 9 V NEPG TFTLES DRP VTVKIQ H BH_10 T RETKVTV NPG EEYEVKV NPG TRVEIQA KGP AEFEG GG TRTRL NPG E SEQ ID NO: 10 SYKFEN LTSQP LRIRLRN LSDTP IEFRIRE E BH_11 S ERREYEV NPG ERMEFTI NKG ERFEEKT NRP MTVRVEL DG REERYTA SEQ ID NO: 11 TPG ESISVQN NSDNP ARVEIQN DSDEP VRVEVRR H BH_12 P IDVRIRM PPG STFRVTI KTD VEVQV NKP VRVEH DG TRTEY KPG THL SEQ ID NO: 12 RI PPG SEVRFEV DTD VEFRFKV TDPETVKEMEEHAREHGL EYETRS D BH_6_ss1 P ERRCIRL SPG ERYTFTV DT PVCFRV EKP VRVRY DG TETEL KPG SHL SEQ ID NO: 13 CL PPG TSITFEV DTP VRFCIQR N BH_6_ss2 P ERREICL SPG ERYTFTV DTP VQFRV EKP VRVRY DG TETEL KPG SHL SEQ ID NO: 14 RL PPG TSITFEV DTP VCFEIQR N BH_6_ss3 P ERREIRL SPG ERYTFTV DTP VQFCV EKP VRVRY DG TETEL KPG SCL SEQ ID NO: 15 RL PPG TSITFEV DTP VR FEIQR N BH_12_ss1 P IDVRICM PPG STFRVTI KTP VEVQV NKP VRVEY DG TRTEL KPG SHL SEQ ID NO: 16 RI PPG SEIRFEV DTP VCFREKV TDPETVKEMEEHAREHGL EYETRS D BH_12_ss2 P IDCRIRM PPG STFRVTI KTP VEVQV NKP VRVEY DG TRTEL KPG SHL SEQ ID NO: 17 RI PPG SEIRFEV DTP VEFREKV TDPETVKEMEEHAREHGL EYECRS D BH_12_ss3 P IDCRIRM PPG STFRVTI KTP VEVQV NKP VRVEY DG TRTEL KPG SHL SEQ ID NO: 18 RI PPG SEIRFEV DTP VEFRFKV TDPETVKECEEHAREHGL EYETRS D BH_13 N CDVRVRV PPG SEVRLTF KTD VRIEV KNP MEVRH DG TETRY TPG THL SEQ ID NO: 19 RI PPG SQVDERV NTD VEFHLEM DNPETAKEVEEQARRQGV EVEVRC Q BH_10_K61V65 T RETKVTVN PG EEYEVKV NPG TRVEIQA KGP AEFEG GG TRTRL NPG E SEQ ID NO: 20 SYKFEN LTSQP LRKRLRV LSDTP IEFRIRE E BH_10_K63V65 T RETKVTVN PG EEYEVKV NPG TRVEIQA KGP AEFEG GG TRTRL NPG E SEQ ID NO: 21 SYKFEN LTSQP LRIRKRV LSDTP IEFRIRE E BH_10_K63 T RETKVTVN PG EEYEVKV NPG TRVEIQA KGP AEFEG GG TRTRL NPG E SEQ ID NO: 22 SYKFEN LTSQP LRIRKRN LSDTP IEFRIRE E BH_10_C6 T RETKCTVN PG EEYEVKV NPG TRVEIQA KGP AEFEG GG TRTRL NPG E SEQ ID NO: 23 SYKFEN LTSQP LRIRLRN LSDTP IEFRIRE E BH_10_C39 T RETKVTVN PG EEYEVKV NPG TRVEIQA KGP AEFEG GG CRTRL NPG E SEQ ID NO: 24 SYKFEN LTSQP LRIRLRN LSDTP IEFRIRE E

In one embodiment, the polypeptide comprises two beta-sheets packing against each other forming a double-stranded beta-helix formed by 8 antiparallel beta-strands, also known as the jelly roll structure, as described in detail in the examples that follow.

In one specific embodiment, the polypeptide comprise an amino acid sequence at least 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% identical to the amino acid sequence selected from the group consisting of SEQ ID NOS: 10, 11, and 20-24.

In another embodiment, amino acid changes from the reference polypeptide do not include changes in proline residues present in the loop connections between beta strands. Loop proline residues help to maintain β-arch structures, as described in the examples that follow.

In a further embodiment, amino acid changes from the reference polypeptide do not include changes in polar amino acid residues present in the loop connections between beta strands capable of forming hydrogen bonds to the loop backbone. As shown in the examples that follow, β-arch loops that are structurally pre-organized with the polar groups making internal hydrogen bonding likely favor folding to the correct topology and contribute to stability by compensating for the loss of interactions with water of polar groups in the sidechains and backbone.

In a still further embodiment, amino acid changes from the reference polypeptide do not include changes in hydrophobic amino acid residues present in the loop connections and adjacent to the polar amino acid residues between beta strands capable of forming hydrogen bonds to the loop backbone. Such hydrophobic residues help stabilize the desired beta sheet structures.

In another embodiment, amino acid changes from the reference polypeptide do not include changes in hydrophobic amino acid residues stabilizing the polypeptide core. Any position with a hydrophobic amino acid corresponds to the polypeptide core.

In another embodiment, amino acid changes from the reference polypeptide are conservative amino acid substitutions.

As used here, “conservative amino acid substitution” means that:

-   -   hydrophobic amino acids (Ala, Cys, Gly, Pro, Met, Sce, Sme, Val,         Ile, Leu) can only be substituted with other hydrophobic amino         acids;     -   hydrophobic amino acids with bulky side chains (Phe, Tyr, Trp)         can only be substituted with other hydrophobic amino acids with         bulky side chains;     -   amino acids with positively charged side chains (Arg, His, Lys)         can only be substituted with other amino acids with positively         charged side chains;     -   amino acids with negatively charged side chains (Asp, Glu) can         only be substituted with other amino acids with negatively         charged side chains; and     -   amino acids with polar uncharged side chains (Ser, Thr, Asn,         Gln) can only be substituted with other amino acids with polar         uncharged side chains.

In all of the above embodiments, the polypeptide may be linked with a detectable label. Any suitable detectable label can be used, including but not limited to fluorescent or bioluminescent proteins, radioactive moieties, etc. In another embodiment, the polypeptide may be immobilized on a surface, including but not limited to a bead, a nanoparticle, a microarray, glass slide, membrane, microplate, etc.

In another aspect the disclosure provides nucleic acids encoding the polypeptide of any embodiment or combination of embodiments of the disclosure. The nucleic acid may comprise single stranded or double stranded RNA or DNA in genomic or cDNA form, or DNA-RNA hybrids, each of which may include chemically or biochemically modified, non-natural, or derivatized nucleotide bases. Such nucleic acid sequences may comprise additional sequences useful for promoting expression and/or purification of the encoded polypeptide, including but not limited to polyA sequences, modified Kozak sequences, and sequences encoding epitope tags, export signals, and secretory signals, nuclear localization signals, and plasma membrane localization signals. It will be apparent to those of skill in the art, based on the teachings herein, what nucleic acid sequences will encode the polypeptides of the disclosure.

In a further aspect, the disclosure provides expression vectors comprising the nucleic acid of any aspect of the disclosure operatively linked to a suitable control sequence. “Expression vector” includes vectors that operatively link a nucleic acid coding region or gene to any control sequences capable of effecting expression of the gene product. “Control sequences” operably linked to the nucleic acid sequences of the disclosure are nucleic acid sequences capable of effecting the expression of the nucleic acid molecules. The control sequences need not be contiguous with the nucleic acid sequences, so long as they function to direct the expression thereof. Thus, for example, intervening untranslated yet transcribed sequences can be present between a promoter sequence and the nucleic acid sequences and the promoter sequence can still be considered “operably linked” to the coding sequence. Other such control sequences include, but are not limited to, polyadenylation signals, termination signals, and ribosome binding sites. Such expression vectors can be of any type, including but not limited plasmid and viral-based expression vectors. The control sequence used to drive expression of the disclosed nucleic acid sequences in a mammalian system may be constitutive (driven by any of a variety of promoters, including but not limited to, CMV, SV40, RSV, actin, EF) or inducible (driven by any of a number of inducible promoters including, but not limited to, tetracycline, ecdysone, steroid-responsive). The expression vector must be replicable in the host organisms either as an episome or by integration into host chromosomal DNA. In various embodiments, the expression vector may comprise a plasmid, viral-based vector, or any other suitable expression vector.

In another aspect, the disclosure provides host cells that comprise the nucleic acids or expression vectors (i.e., episomal or chromosomally integrated) disclosed herein, and/or a cell expressing the polypeptide of any embodiment or combination of embodiments herein, wherein the host cells can be either prokaryotic or eukaryotic. The cells can be transiently or stably engineered to incorporate the expression vector of the disclosure, using techniques including but not limited to bacterial transformations, calcium phosphate co-precipitation, electroporation, or liposome mediated-, DEAE dextran mediated-, polycationic mediated-, or viral mediated transfection.

In another embodiment, the disclosure provides pharmaceutical compositions comprising:

(a) the polypeptide, nucleic acid, expression vector, host cell, or cell of any embodiment or combination of embodiments herein; and

(b) a pharmaceutically acceptable carrier.

The pharmaceutical compositions of the disclosure can be used, for example, in the methods of the disclosure described below. The pharmaceutical composition may comprise in addition to the polypeptide or other active agent of the disclosure (a) a lyoprotectant; (b) a surfactant; (c) a bulking agent; (d) a tonicity adjusting agent; (e) a stabilizer; (f) a preservative and/or (g) a buffer.

In some embodiments, the buffer in the pharmaceutical composition is a Tris buffer, a histidine buffer, a phosphate buffer, a citrate buffer or an acetate buffer. The pharmaceutical composition may also include a lyoprotectant, e.g. sucrose, sorbitol or trehalose. In certain embodiments, the pharmaceutical composition includes a preservative e.g. benzalkonium chloride, benzethonium, chlorohexidine, phenol, m-cresol, benzyl alcohol, methylparaben, propylparaben, chlorobutanol, o-cresol, p-cresol, chlorocresol, phenylmercuric nitrate, thimerosal, benzoic acid, and various mixtures thereof. In other embodiments, the pharmaceutical composition includes a bulking agent, like glycine. In yet other embodiments, the pharmaceutical composition includes a surfactant e.g., polysorbate-20, polysorbate-40, polysorbate-60, polysorbate-65, polysorbate-80 polysorbate-85, poloxamer-188, sorbitan monolaurate, sorbitan monopalmitate, sorbitan monostearate, sorbitan monooleate, sorbitan trilaurate, sorbitan tristearate, sorbitan trioleaste, or a combination thereof. The pharmaceutical composition may also include a tonicity adjusting agent, e.g., a compound that renders the formulation substantially isotonic or isoosmotic with human blood. Exemplary tonicity adjusting agents include sucrose, sorbitol, glycine, methionine, mannitol, dextrose, inositol, sodium chloride, arginine and arginine hydrochloride. In other embodiments, the pharmaceutical composition additionally includes a stabilizer, e.g., a molecule which, when combined with a protein of interest substantially prevents or reduces chemical and/or physical instability of the protein of interest in lyophilized or liquid form. Exemplary stabilizers include sucrose, sorbitol, glycine, inositol, sodium chloride, methionine, arginine, and arginine hydrochloride.

The polypeptides, nucleic acids, expression vectors, host cells, and/or cells may be the sole active agent in the pharmaceutical composition, or the composition may further comprise one or more other active agents suitable for an intended use.

The polypeptides, nucleic acids, expression vectors, host cells, cells, and/or pharmaceutical compositions of the disclosure may be used for any suitable purpose, including but not limited to as scaffolds for virus capsids and antibodies; to transport hydrophobic molecules; for use in recognition and enzymatic processing of carbohydrates; or for incorporating metal, ligand-binding and active sites. Details are provided in the examples that follow.

In another aspect, the disclosure provides methods for designing polypeptides that form a double-stranded β-helix formed by 8 antiparallel β-strands, comprising the steps of any embodiment or combinations of embodiments disclosed herein. Details of exemplary design methods are provided in the examples that follow.

The description of embodiments of the disclosure is not intended to be exhaustive or to limit the disclosure to the precise form disclosed. While the specific embodiments of, and examples for, the disclosure are described herein for illustrative purposes, various equivalent modifications are possible within the scope of the disclosure, as those skilled in the relevant art will recognize.

Examples Summary

β-sheet proteins carry out critical functions in biology, and hence are attractive scaffolds for computational protein design. Despite this potential, de novo design of all β-sheet proteins from first principles lags far behind the design of all-α or mixed αβ domains due to their non-local nature and tendency of exposed β-strand edges to aggregate. Through study of loops connecting unpaired β-strands (β-arches), we have identified a series of structural relationships between loop geometry, sidechain directionality and β-strand length that arise from hydrogen bonding and packing constraints on regular β-sheet structures. We use these rules to de novo design jelly-roll structures with double-stranded β-helices formed by 8 antiparallel β-strands. The structure of a hyperthermostable design closely matched the computational model, demonstrating accurate control over the β-sheet structure and loop geometry. Our results open the door to the design of a broad range of non-local β-sheet protein structures.

Results Constraints on β-Arch Geometry

We undertook the investigation of the constraints on the backbone geometry of β-strands and connecting loops that arise from hydrogen bonding and the requirement for a compact hydrophobic core. We studied sidechain directionality patterns of the two β-strand residues adjacent to β-arch loops (FIG. 1A, left) in naturally occurring protein structures, defining the sidechain orientation of the β-strand residue preceding the loop as concave (represented by “↓”) if its CαCβ vector is parallel to the vector d from the first to the second β-strand, and convex (represented by “↑”) if the CαCβ vector is antiparallel to d. For the residue following the loop the sidechain pattern is described in the same way, but instead using the vector from the second to the first β-strand (-d) as a reference (FIG. 1A). This results in four possible β-arch loop sidechain orientation patterns: “↑↑”, “↑↓”, “↓↑” and “↓↓”. We analyzed the sidechain patterns and the local backbone geometry—as described with ABEGO torsion bins¹⁶—of 5,061 β-arch loops from a non-redundant database of natural protein structures (torsion bins “A” and “B” are the α-helix and extended regions, “G” and “E” regions are the positive φ angle equivalents of “A” and “B”; and “O” is the cis peptide bond conformation; FIG. 4). We found that all four sidechain orientation patterns frequently occur, and, in contrast to other types of loop connections (i.e. αβ, βα and β-hairpins)⁵, there was not a correlation between β-arch loop length and sidechain pattern. Instead, each loop ABEGO type, because of the way in which it twists and bends the polypeptide chain¹⁶, is associated with a specific flanking residue sidechain pattern (FIG. 1C). The most frequently observed turn types (between 1 and 5 amino acids) for each sidechain pattern are listed in FIG. 1D-E; for example ABB, BBGB, BABB and BGB are the most frequent loop types for the patterns “↓↓”, “↓↑”, “↑↓” and “↑↑”, respectively.

The next level of non-local interaction complexity in all-β folds involves strand pairing (parallel or antiparallel) between two β-arches forming a β-arcade (FIG. 1F). Since the β-arch loops are stacked in-register, the sidechains adjacent to one β-arch loop are likely to have the same orientation as the sidechains adjacent to the second β-arch loop; analysis of naturally occurring β-arcades confirms that the sidechain patterns of the two β-arch loops indeed are correlated (FIG. 1G).

Jelly-Roll Design Principles

The double-stranded β-helix can be regarded as a long β-hairpin wrapped around an axis perpendicular to the direction of β-strands, with β-helical turns formed by the pairing between β-arcades (FIG. 2A). In the compact folded structure, two antiparallel β-sheets pack against each other in a sandwich-like arrangement, with the first strand paired to the last, and all β-strands are connected through β-arch loops except for the central β-hairpin. We aimed at designing β-helices with 3 β-arcades forming two antiparallel 4-stranded β-sheets, with the 8 β-strands connected through 6 β-arches and 1 β-hairpin. The non-local character of the structure grows from the first β-arcade, which starts from the central β-hairpin, to the last one, where the N- and C-termini are paired.

The analysis from FIG. 1 leads to strong constraints on the construction of β-sheet backbone structures, as the sidechain directionality patterns of the β-strands and loops are coupled in several ways. First, the directionality patterns of the loops preceding and following each β-strand are coupled to the length of the strand (FIG. 2B): for example, a β-strand with an even number of residues that is preceded by a “↑↑” loop must be followed by a “↓↑” or a “↓↓” loop, but not a “↑↑” or “↑↓” loop, due to the alternating pleating of β-strands. Second, since the β-arcades of the β-helix have paired β-strands and β-arch loops, the sidechains adjacent to one β-arch loop must have the same orientation as the paired sidechains adjacent to the second β-arch loop (FIG. 1F). Due to the antiparallel orientation of the β-arcades, “↓↓” and “↑↑” loops are compatible with loops of the same type, but “↑↓“loops are only compatible with” ↓↑” (FIG. 1F). Third, the twist and curvature of the two β-sheets of the β-helix is constrained by the hydrogen bonding register between β-arcades 1 and 3 (herein called β-arcade register), and within β-strand pairs S₃/S₈ and S₄/S₇, as shown in FIG. 2C.

De Novo Design of Protein Structures

We constructed double-stranded β-helix protein backbones by Monte Carlo fragment assembly using blueprints—representations of the target protein topologies specifying the ordering, lengths and backbone torsion bins of secondary structure elements and loop connections⁵—in conjunction with backbone hydrogen-bonding constraints specifying all pairings between β-strands. We explored strand lengths between 5 and 7 residues and the most commonly observed β-arch loops between 3 and 5 residues (FIG. 1D). The central β-hairpin was designed with two-residue loops following the ββ-rule⁵. The register shifts between pairs of β-strands from different β-arcades (1 and 3) were allowed to range from 0 to 2 and the β-arcade register shifts between 0 and 4; strand pairs within the same β-arcade were kept in-register. A total of 3,673 combinations were enumerated, of which 1,853 had mutually compatible strand lengths and loop types consistent with the constraints summarized in the previous paragraph. For each of these internally consistent blueprints, we used Rosetta™ to build thousands of protein backbones. The resulting ensemble of backbone structures has considerable structural diversity; those with all strands in-register had narrow sandwich-like structures (FIG. 2D), while those with large register shifts had wider barrel-like structures (FIG. 2E).

For each generated backbone, we carried out flexible-sequence design calculations to identify low-energy amino acid identities and sidechain conformations providing close complementary packing, sidechain-backbone hydrogen bonding in β-arch loops—to pre-organize their conformation and facilitate folding—and high sequence-structure compatibility. We favored inward-pointing charged or polar amino acids at the four edge strands to minimize aggregation propensity. Loop sequences were designed with consensus profiles obtained from fragments with the same backbone ABEGO torsion bins²¹. Because the very large size of the space sampled by our design procedure limits convergence on optimal sequence-structure pairs, we carried out a second round of calculations starting from the blueprints yielding the lowest energy designs, intensifying sampling at both the backbone and sequence level. For a subset of designs, we introduced disulfide bonds between paired β-strand positions with high sequence separation (e.g. between the first and last β-strands) and optimal orientation (see Methods) —disulfide bonds distant in primary sequence decrease the entropy of the unfolded state and therefore enhance the thermodynamic stability of the native state. To assess compatibility of the top ranked designed sequences with their structures we characterized their folding energy landscape with biased forward folding simulations, and those with substantial near-native sampling were subsequently assessed by Rosetta™ ab initio structure prediction calculations. Designs with funnel-shaped energy landscapes—where the designed structure is at the global energy minima and has a substantial energy gap with respect to alternative conformations—were selected for experimental characterization. Ab initio structure prediction of natural β-sheet proteins tends to oversample local contacts (i.e. favoring β-hairpins over β-arches), but we succeeded in designing sequences with the β-arches sufficiently strongly encoded that they folded in silico to near the designed target structure.

Experimental Characterization

We chose for experimental characterization 19 designs with funnel-shaped energy landscapes ranging between 70 and 94 amino acids (Table 2). BLAST searches^(26,27) indicated that the designed sequences had little or no similarity with native proteins (lowest E-values ranging from 0.003 to >10; Table 3). Synthetic genes encoding the designs (design names are BH_n; where “BH” stands for β-helix and “n” the design number; and a “_ss” suffix if disulfide bonds are present) were obtained, the proteins were expressed in Escherichia coli, and purified by affinity chromatography. 16 of the designs expressed well and were soluble, and two (BH_10 and BH_11) were monomeric (FIG. 5) by size-exclusion chromatography coupled with multi-angle light scattering (SEC-MALS) (most of the non-monomeric designs were either dimers or soluble aggregates). Both monomeric designs had far-ultraviolet circular dichroism spectrum (CD) at 25° C. characteristic of β proteins and a melting temperature (T_(m)) above 95° C. (FIG. 3A-B and FIG. 6).

TABLE 2  Designed protein sequences. The lowest E-value obtained from BLAST searches (against the NCBI nr database of  non-redundant protein sequences) is shown. Design name Amino acid sequence E-value BH_1 P ETKTYRF TPG EEREYE ENT DVEVEV NHD MEITV NG QTQRY TPG TSV 3.2 SEQ ID NO: 1 RV PPG SRVRIRV NDD VKVNWHE R BH_2 Q HTRTYRL TPG EEQEFKY NTP MTMHVEV NTD VEIEY NG KEQRY PPG T 2.8 SEQ ID NO: 2 EVEIEVR PGT KVRIKV NTD VRVEIRE N BH_3 P ETRTYRF TPG EEREFEF DTN VEFRF DSD VEVTV NG QTTRV PPG SSV 1.1 SEQ ID NO: 3 EV PPG SRIRIRV NTD LQVEVRR R BH_4 P ETRTYRF TPG EEREFEH DTN VKWKF NTD VEIER NG ERTRF TPG EEV 3.6 SEQ ID NO: 4 EV PPG TRVRIRV NTD VQFTLER N BH_5 P ERREIRL SPG ERYTFTV DTD VQFRV EKP VRVRH DG TETEY KPG THL 0.016 SEQ ID NO: 5 RL PPG TSVTFEV DTD VRFEIQR N BH_6 P ERREIRL SPG ERYTFTV DTP VQFRV EKP VRVRY DG TETEL KPGSHL 0.011 SEQ ID NO: 6 RL PPG TSITFEV DTP VR FEIQR N BH_7 S RYEITG NPG TRVELRE NPG SRVKS NAPG RSER NG EHRTW NPG ESRT 0.8 SEQ ID NO: 7 S NRP STMEVES DGP ISIEIR E BH_8 E SKKITV NAGER MTLHL NAG TEVRS EGP GREHS NG QTQQW PPG STIR 3.5 SEQ ID NO: 8 S DQP TTTTF ESDRP LTLEVR Q BH_9 K TKTYTV NPGE KVTITM NPG DEMTA EGP VTSRA RG QEQTV NPG ETVR >10 SEQ ID NO: 9 V NEPG TFTLES DRP VTVKIQ H BH_10 T RETKVTVN PG EEYEVKV NPG TRVEIQA KGP AEFEG GG TRTRL NPG E 6.3 SEQ ID NO: 10 SYKFEN LTSQP LRIRLRN LSDTP IEFRIRE E BH_11 S ERREYEV NPG ERMEFTI NKG ERFEEKT NRP MTVRVEL DG REERYTA 4.5 SEQ ID NO: 11 TPG ESISVQN NSDNP ARVEIQN DSDEP VRVEVRR H BH_12 P IDVRIRM PPG STFRVTI KTD VEVQV NKP VRVEH DG TRTEY KPG THL 1.0 SEQ ID NO: 12 RI PPG SEVRFEV DTD VEFREKV TDPETVKEMEEHAREHGL EYETRS D BH_6_ss1 P ERRCIRL SPG ERYTFTV DT PVCFRV EKP VRVRY DG TETEL KPG SHL 0.013 SEQ ID NO: 13 CL PPG TSITFEV DTP VRFCIQR N BH_6_ss2 P ERREICL SPG ERYTFTV DTP VQFRV EKP VRVRY DG TETEL KPG SHL 0.003 SEQ ID NO: 14 RL PPG TSITFEV DTP VCFEIQR N BH_6_ss3 P ERREIRL SPG ERYTFTV DTP VQFCV EKP VRVRY DG TETEL KPG SCL 0.012 SEQ ID NO: 15 RL PPG TSITFEV DTP VR FEIQR N BH_12_ss1 P IDVRICM PPG STFRVTI KTP VEVQV NKP VRVEY DG TRTEL KPG SHL 0.98 SEQ ID NO: 16 RI PPG SEIRFEV DTP VCFREKV TDPETVKEMEEHAREHGL EYETRS D BH_12_ss2 P IDCRIRM PPG STFRVTI KTP VEVQV NKP VRVEY DG TRTEL KPG SHL 6.8 SEQ ID NO: 17 RI PPG SEIRFEV DTP VEFREKV TDPETVKEMEEHAREHGL EYECRS D BH_12_ss3 P IDCRIRM PPG STFRVTI KTP VEVQV NKP VRVEY DG TRTEL KPG SHL 7.7 SEQ ID NO: 18 RI PPG SEIRFEV DTP VEFRFKV TDPETVKECEEHAREHGL EYETRS D BH_13 N CDVRVRV PPG SEVRLTF KTD VRIEV KNP MEVRH DG TETRY TPG THL 1.9 SEQ ID NO: 19 RI PPG SQVDFRV NTD VEFHLEM DNPETAKEVEEQARRQGV EVEVRC Q

The two monomeric designs with well-ordered structures were among those with better packed cores and a larger proportion of β-arch loops containing prolines and hydrogen bonding satisfying the backbone polar atoms (Table 3). β-arch loops that are structurally pre-organized with the polar groups making internal hydrogen bonding likely favor folding to the correct topology and contribute to stability by compensating for the loss of interactions with water of polar groups in the sidechains and backbone. These interactions could also disfavor the competing local strand pairing arrangement in which the two strands form a β-hairpin—this is a very common pathology in ab initio structure prediction²⁵. For the most stable dimeric design (BH_6) we introduced disulfide bonds to stabilize protein regions having contacts with large sequence separation—e.g. between the N- and C-terminal strands—but this did not succeed in yielding stable monomers. Addition of an α-helix to the C-termini (one of the two extremes of the β-helix) as a capping domain protecting the strand edges from inter-molecular pairing also failed to yield stable monomers, even in combination with disulfide bonds. This suggests that the sequence of the core β-sheet must strongly encode its structure independent of disulfide bonds or protecting domains aimed at increasing stability.

TABLE 3 Computed scores for experimentally characterized designs. Hydrogen bonding (hbond_bb_sc, hbond_lr_bb and hbond_sr_bb) and backbone torsional (rama) energy scores were averaged over all loop residue positions, and the fa_atr score term accounting for attractive Van der Waals interactions was averaged over all residues. Designs in the table were ranked based on “hbond_sum” (sum of the three hydrogen bonding average scores), rama and “loops w/Pro” (number of loops containing at least one proline). Designs with substantially higher fa_atr scores (indicative of underpacked hydrophobic cores) were placed at the end of the ranking (BH_7, BH_9 and BH_8). Only those designs without disulfide bonds or extra helical domains were considered in this analysis. The two monomeric designs with well-ordered structures (BH_10 and BH_11) are those with the best compromise of the three scores considered. Design loops name hbond_sum hbond_bb_sc hbond_lr_bb hbond_sr_bb rama w/Pro fa_atr BH_11 −0.651 −0.220 −0.328 −0.103 −0.161 5 −4.510 BH_10 −0.556 −0.109 −0.348 −0.099 −0.142 6 −4.334 BH_2 −0.557 −0.120 −0.391 −0.046 −0.138 4 −4.557 BH_1 −0.545 −0.086 −0.406 −0.053 −0.150 3 −4.609 BH_3 −0.547 −0.076 −0.429 −0.042 −0.113 3 −4.367 BH_6 −0.531 −0.073 −0.396 −0.061 −0.085 6 −4.478 BH_4 −0.515 −0.055 −0.337 −0.124 −0.137 3 −4.679 BH_5 −0.535 −0.077 −0.395 −0.063 −0.088 4 −4.575 BH_7 −0.617 −0.162 −0.333 −0.122 −0.125 6 −3.691 BH_9 −0.557 −0.094 −0.344 −0.120 −0.104 6 −3.652 BH_8 −0.622 −0.150 −0.338 −0.134 −0.087 4 −3.842

Structure of a De Novo Designed β-Helix

The structure of BH_10 was confirmed by NMR spectroscopy (data not shown) and found it to be in very close agreement with the computational model (Cα-RMSD 0.84 Å, data not shown). The overall topology is accurately recapitulated, including all strand pairings, register shifts and loop connections. The designed aliphatic and aromatic sidechain packing in the protein core as well as salt bridge interactions across the two β-sheet surfaces were also accurately reproduced—three salt bridges between the two paired β-arcades and one within the third β-arcade are well supported (FIG. 7). The agreement both in the backbone conformation and hydrogen-bonding interactions of the loops forming the three β-arcades is remarkable, given that these elements are the most flexible parts of the structure and therefore difficult to design due to sampling bottlenecks. The β-arcades were designed with pairs of β-arch loops that mutually interact via backbone-backbone hydrogen bonds—due to the complementarity between their backbone conformations—stabilizing loop pairing and avoiding burial of polar backbone atoms (see FIG. 8 for the BH_10 loop sequences and sidechain patterns). For example, β-arcade 1 is formed by ‘BBG’ and ‘ABB’ loops, and the buried backbone NH group of the ‘G’ position in the former makes a hydrogen bond with the buried backbone C═O of the neighboring loop (FIG. 3D). The other two β-arcades were designed with one β-arch loop containing buried and fully hydrogen-bonded asparagines (4 hydrogen bonds in total) that stabilize both loop pairing and the local β-arch conformation (of ‘ABABB’ loops) (FIG. 3E). By design, the asparagine sidechain geometry was further stabilized with hydrophobic stacking interactions from the two β-arch loops of the same arcade.

The amino acid sequence of BH_10 is unrelated to any sequence in the NCBI nr database. We searched the PDB for similarities in structure or sequence (with HHpred³⁰ for sensitive profile based sequence search), and identified matches similar in fold but containing additional and irregular secondary structures, and longer loops. These matches are all homodimers with sheet-to-sheet interface packing (FIG. 9) or domains integrated in larger structures, in sharp contrast to the BH_10 monomer.

Contact Order and Sequence Determinants of the BH_10 Fold

The non-local character of BH_10 is of particular note—a large fraction of the contacting residues are distant along the linear sequence, with extensive strand pairing between the N and C-terminal β-strands. The contact order of the structure—the average separation along the linear sequence of residues in contact in the three dimensional structure—is higher than any previous single-domain protein designed de novo (FIG. 3F-G). High contact order proteins fold more slowly than low contact order proteins as there is a greater loss in chain entropy for forming the first native interactions, and they tend to form long-lived non-native structures that can oligomerize or aggregate³¹. We have overcome the challenges in designing non-local structures by focusing on backbones lacking internal strain and having maximal internal coherence, and programming β-strand orientation with highly structured loops.

One of the challenges in achieving high contact order through β-arches is to disfavor competing more sequence-local β-hairpins. To evaluate in silico how each of our design features contribute to favoring β-arches over β-hairpins, we generated folding energy landscapes for a series of mutants of BH_10 that disrupt, one at a time, loop hydrogen bonding, sidechain packing of loop neighbors and loop local geometry. For all conformations generated, we classified all the β-strand connections as β-arch or β-hairpin depending on strand pairing formation, and calculated the overall frequency of β-hairpin formation for each pair of consecutive β-strands. As shown in FIG. 10, disruption of packing within or between β-arch loops, removal of sidechain-backbone hydrogen bonding interactions and reducing loop geometry encoding by eliminating prolines all increase sampling of competing β-hairpin conformations, and thus substantially decrease sampling of β-arches and the target designed structure.

Discussion

The design of all-β globular proteins from first principles has remained elusive for two decades of protein design research. We have successfully designed a double-stranded β-helix de novo, as confirmed by structure studies of the design BH_10, based on a series of rules describing the geometry of β-arch loops and their interactions in more complex β-arcades. Our work also achieves two related milestones: the first accurate design of an all-β globular protein with exposed β-sheet edges, and the most non-local structure yet designed from scratch. Comparison between successful and failed designs suggests folding and stabilization of the monomeric structure (and implicitly, disfavoring of competing topologies with more local strand pairings) is bolstered by loops containing sidechain-backbone and backbone-backbone hydrogen bonds together with well-packed mixed aliphatic/aromatic sidechains in the protein core, inward-pointing polar amino acids at strand edges and salt bridges between paired strands. The β-helix fold here designed is well suited for incorporating metal, ligand-binding and active sites. With the basic design principles now understood, our de novo design strategy should enable the construction of a wide range of β-helix structures tailored to a broad diversity of target ligands.

The design rules described here are a considerable advance as they provide control over β-arch connections between distinct β-sheets, and enable the design of a broad range of β-protein families beyond the β-barrel and β-helix with considerable medical and biotechnological potential; for example the immunoglobulin fold widely utilized for binding and loop scaffolding in nature is topologically very similar to the double-stranded β-helices designed here, with a larger proportion of β-hairpins over β-arches.

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Methods

Loop analysis. Loop connections between β-strands were collected from a non-redundant database of PDB structures obtained from the PISCES™ server³² with sequence identity <30% and resolution ≤2 Å. We discarded those loops connecting β-strands with hydrogen bonded pairing (β-hairpins), and the remaining 5,061 β-arch loops were subsequently analyzed. The ABEGO torsion bins of each residue position were assigned based on the definition shown in FIG. 4, and the sidechain directionality pattern of neighboring residues was defined according to FIG. 1A. The secondary structure of all residue positions was assigned with DSSP and the last β-strand residue preceding and the first β-strand residue following the β-arch loop were chosen as the critical neighboring residues determining the sidechain pattern of the loop. The loop bending was defined as the angle between the loop center of mass and the two strand positions adjacent to the loop. Those loops with bending angles larger than 120 degrees were discarded from the analysis to correctly identify those loops producing a substantial change in the direction of the two connected β-strands.

Backbone generation. We used the Blueprint Builder™ mover of RosettaScripts™ to build protein backbones by Monte Carlo fragment assembly using 9- and 3-residue fragments compatible with the target secondary structure and torsion bins (ABEGO), as specified in the blueprints of every target topology. We used a poly-valine centroid representation of the protein and a scoring function accounting for backbone hydrogen bonding, Van der Waals interactions (namely to avoid steric clashes), planarity of the peptide bond (omega score term), and compacity of structures (radius of gyration). Thousands of independent folding trajectories are performed and subsequently filtered. Due to the non-local character of β-sheet contacts, we used distance and angle constraints to favor the correct hydrogen bonded pairing between β-strands main chain atoms. For every target topology we automatically set all pairs of residues involved in β-strand pairing to generate all constraints for backbone building. Protein backbones were filtered based on their match with the blueprint specifications (secondary structure, torsion bins and strand pairing), and subsequently ranked based on backbone hydrogen bonding energy (lr_hb score term), and the total energy obtained from one round of all-atom flexible-sequence design (see below)

Flexible sequence design. Generated protein backbones were subjected to flexible-sequence design calculations with RosettaDesign™ using the Rosetta™ all-atom energy function “Talaris2014” to favor amino acid identities and side-chain conformations with low-energy and tight packing. We performed cycles of fixed backbone design followed by backbone relaxation using the FastDesign mover of RosettaScripts™. Designed sequences were filtered based on total energy, sidechain packing (measured with RosettaHoles™, packstat and core side-chain average degree), sidechain-backbone hydrogen bond energy, and secondary structure prediction (match between the designed secondary structure and that predicted by Psipred based on the designed sequence). Amino acid identities were restricted based on the solvent accessibility of protein positions, ensuring that hydrophobic amino acids are located in the core and polars in the surface. Further restrictions were imposed to improve sequence-structure compatibility in loop regions. Sequence profiles were obtained for naturally occurring loops with the same ABEGO string sequence, as done previously²¹.

For those blueprints that yielded the lowest energy designs we performed a second round with ten times more backbone samples. Backbones generated in this second round were subjected to more exhaustive sequence design by running multiple Generic Monte Carlo trajectories optimizing total energy and sidechain average degree simultaneously, and then applied all filters described above.

Design of disulfide bonds and helix capping domain. We used the Disulfidize mover of RosettaScripts™ to identify pairs of residue positions able to form disulfide bonds with a good scoring geometry. We searched for disulfide bonds between residues distant in primary sequence and with a disulfide score <−1.0. We designed a C-terminal helix capping domain (followed with a β-strand pairing with the first β-strand) using the backbone generation protocol described above but starting from design BH_6. The structure of BH_6 was kept fixed during fragment assembly and the C-terminal domain was generated. Then sequence design was performed for the C-terminal domain and those neighboring residues within 10 Å.

Sequence-structure compatibility. For assessing the local compatibility between designed sequences and structures we picked 200 naturally occurring fragments (9- and 3-mers) with sequences similar to the design and evaluated the structural similarity (by RMSD) between the ensemble of picked fragments and the local designed structure. Those with overall low RMSD fragments, and therefore with high fragment quality, were subsequently assessed by Rosetta™ folding simulations using the Rosetta™ energy function “ref2015”. First, biased forward folding simulations (using the three-lowest RMSD fragments and 40 folding trajectories) were used to quickly identify those designs more likely to have funnel-shaped energy landscapes. Those designs achieving near-native sampling (RMSD to target structure below 1.5 Å) were then assessed by standard Rosetta™ ab initio structure prediction.

To evaluate the amount of β-hairpin sampling in each loop connection during ab initio structure prediction we first detected all strand pairings formed in each generated decoy and then mapped the residues involved in those strand pairings to the secondary structure elements of the designed structure. After secondary structure mapping, pairings between strands consecutive in the sequence were counted as β-hairpins. The total count of β-hairpins sampled in each loop over the total number of generated decoys is a relative quantity of hairpin sampling that allowed to compare the β-hairpin propensity of different loops and mutants, as shown in FIG. 9.

Contact order. To evaluate the non-local character of protein structures we computed contact order as the average sequence separation between pairs of Ca atoms within a distance of 8 Å and with a sequence separation of 3 residues at least.

Protein expression and purification. Genes encoding the designed sequences were obtained from Genscript and cloned into the pET-28b+ (with N-terminal 6×His tag and a thrombin cleavage site) expression vectors. Plasmids were transformed into Escherichia coli BL21 Star™ (DE3) competent cells, and starter cultures were grown at 37° C. in Luria-Bertani (LB) medium overnight with kanamycin. Overnight cultures were used to inoculate 500 ml of LB medium supplemented with antibiotic and cells were grown at 37° C. and 225 r.p.m until an optical density (OD600) of 0.5-0.7 was reached. Protein expression was induced with 1 mM of isopropyl β-D-thiogalactopyranoside (IPTG) at 18° C. and, after overnight expression, cells were collected by centrifugation (at 4° C. and 4400 r.p.m for 10 minutes) and resuspended in 25 ml of lysis buffer (20 mM imidazole and phosphate buffered saline, PBS). Resuspended cells were lysed in the presence of lysozyme, DNAse and protease inhibitors. Lysates were centrifuged at 4° C. and 18,000 r.p.m. for 30 minutes; and the supernatant was loaded to a nickel affinity gravity column pre-equilibrated in lysis buffer. The column was washed with three column volumes of PBS+30 mM imidazole and the purified protein was eluted with three column volumes of PBS+250 mM imidazole. The eluted protein solution was dialyzed against PBS buffer overnight. The expression of purified proteins was assessed by SDS-polyacrylamide gel electrophoresis and mass spectrometry; and protein concentrations were determined from the absorbance at 280 nm measured on a NanoDrop™ spectrophotometer (ThermoScientific) with extinction coefficients predicted from the amino acid sequences using the ProtParam™ tool. Proteins were further purified by FPLC size-exclusion chromatography using a Superdex™ 75 10/300 GL (GE Healthcare) column.

Circular dichroism (CD). Far-ultraviolet CD measurements were carried out with the AVIV 420 spectrometer. Wavelength scans were measured from 260 to 195 nm at temperatures between 25 and 95° C., using a 1 mm path-length cuvette. Protein samples were prepared in PBS buffer (pH 7.4) at a concentration of 0.2-0.4 mg/mL.

Size exclusion chromatography combined with multiple angle light scattering (SEC-MALS). SEC-MALS experiments were performed using a Superdex™ 75 10/300 GL (GE Healthcare) column combined with a miniDAWN™ TREOS multi-angle static light scattering detector and an Optilab T-rEX™ refractometer (Wyatt Technology). One hundred microliter protein samples of 1-3 mg/ml were injected to the column equilibrated with PBS (pH 7.4) or TBS (pH 8.0) buffer at a flow rate of 0.5 ml/min. The collected data was analyzed with ASTRA™ software (Wyatt Technology) to estimate the molecular weight of the eluted species.

Protein expression of isotopically labeled proteins for structure determination. Plasmids were transformed using standard heat shock transformation into Lemo21 expression strain of E. coli (NEB) and plated onto a minimal M9 media containing glucose and kanamycin to maintain tight control over expression. A single colony was selected, inoculated into 50 mL of Luria Broth containing 50 ug/mL of kanamycin and grown at 37° C. with shaking overnight. After approximately 18 hours, the 50 mL starter culture was removed and 25 mL was used to inoculate 500 mL of Terrific Broth™ containing 50 ug/mL kanamycin and mixed mineral salts. The Terrific Broth™ (TB) culture was grown at 37° C. with shaking at 250 rpm until OD600 reached a value of 1.0. At this time the culture was removed and the cells were pelleted by centrifugation at 4000 rpm for 15 minutes. The TB broth was removed and the pelleted cells were resuspended gently with 50 mL of 20 mM NaPO4 150 mM NaCl pH 7.5. The resuspended cells were transferred into minimal labeling media, containing N15 labelled Ammonium Chloride at 50 mM and C13 glucose to 0.25% (w/v), as well as trace metals, 25 mM Na₂HPO₄, 25 mM KH₂PO₄, and 5 mM Na₂SO₄. The culture was returned to 37° C., at 250 rpm for 1 hour in order to replace unlabeled Nitrogen and Carbon with labelled Nitrogen and Carbon. After 1 hour, IPTG was added to 1 mM, the temperature was reduced to 25° C. and the culture allowed to express overnight. The following morning the culture was removed and the cells were pelleted by centrifugation at 4000 rpm for 15 minutes. The cells were resuspended with 40 mL of Lysis Buffer (20 mM Tris 250 mM NaCl 0.25% Chaps pH 8) and lysed with a Microfluidics M110P Microfluidizer at 18000 psi. The lysed cells were clarified using centrifugation at 24000×g for 30 minutes. The labelled protein in the soluble fraction was purified using Immobilized Metal Affinity Chromatography (IMAC) using standard methods (Qiagen Ni-NTA resin). The purified protein was then concentrated to 2 mL and purified by FPLC size-exclusion chromatography using a Superdex™ 75 10/300 GL (GE Healthcare) column into 20 mM NaPO4 150 mM NaCl pH 7.5. The efficiency of labelling was confirmed using mass spectrometry.

Visualization of protein structures and image rendering. Images of protein structures were created with PyMOL.

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We claim:
 1. A polypeptide comprising an amino acid sequence at least 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% identical to the amino acid sequence selected from the group consisting of SEQ ID NOS:1-24, wherein the polypeptide forms a beta-sheet.
 2. The polypeptide of claim 1, wherein the polypeptide comprises two beta-sheets packing against each other forming a double-stranded beta-helix formed by 8 antiparallel beta-strands.
 3. The polypeptide of claim 1, wherein the polypeptide comprises an amino acid sequence at least 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, 99%, or 100% identical to the amino acid sequence selected from the group consisting of SEQ ID NOS:10, 11, and 20-24.
 4. The polypeptide of claim 1, wherein amino acid changes from the reference polypeptide do not include changes in proline residues present in loop connections between beta strands.
 5. The polypeptide of claim 1, wherein amino acid changes from the reference polypeptide do not include changes in polar amino acid residues present in loop connections between beta strands capable of forming hydrogen bonds to the loop backbone.
 6. The polypeptide of claim 5, wherein amino acid changes from the reference polypeptide do not include changes in hydrophobic amino acid residues present in the loop connections and adjacent to the polar amino acid residues between beta strands capable of forming hydrogen bonds to the loop backbone.
 7. The polypeptide of claim 1, wherein amino acid changes from the reference polypeptide do not include changes in hydrophobic amino acid residues stabilizing the polypeptide core.
 8. The polypeptide of claim 1, wherein amino acid changes from the reference polypeptide are conservative amino acid substitutions.
 9. The polypeptide of claim 1 linked to a detectable label and/or immobilized on a surface.
 10. A nucleic acid encoding the polypeptide of claim
 1. 11. An expression vector comprising the nucleic acid of claim 7 operatively linked to a control sequence.
 12. A host cell comprising the nucleic acid of claim 7 and/or an expression vector comprising the nucleic acid.
 13. A cell expressing the polypeptide of claim
 1. 14. A pharmaceutical composition comprising: (a) the polypeptide of claim 1; and (b) a pharmaceutically acceptable carrier.
 15. Use of the polypeptide of claim 1 for any suitable purpose, including but not limited to as scaffolds for virus capsids and antibodies and to transport hydrophobic molecules, for use in recognition and enzymatic processing of carbohydrates; incorporating metal, ligand-binding and active sites.
 16. A method for designing polypeptides that form a double-stranded β-helix formed by 8 antiparallel β-strands, comprising the steps of any embodiment or combinations of embodiments disclosed herein. 